Research shows that the use of interdisciplinary units in teaching skills is more effective than teaching skills in isolation. Eliminating content isolation helps students recognize the interconnectedness of subjects. Euler, Descartes, Escher, Pascal, Plato, Carroll, Dudeney, and Loyd are examples of ancient to contemporary individuals who made contributions to the study of mathematics. Discovering the history of the person, playing with their mathematics, and reporting the findings can be incorporated into exciting activities. The objective of this session is to make teachers comfortable with combining these elements into meaningful activities. They receive examples of activities from these historic personalities

Scarsdale is going to abandon TRAILBLAZERS it seems. Nothing bad should be said about TRAILBLAZERS, however! TRAILBLAZERS isn't bad! Scarsdale is merely continuing ever onward in its eternal journey of excellence. (My friend is sending the article; I'll have the actual quote shortly.)

Yesterday, my 5th grader came home with three multiplication quizzes that her class had done in class.

The first quiz was the three’s tables. 3 x 1 = ___, 3 x 2 = ___, 3 x 3 = ___, etc. up to 12. The next two quizzes covered the four’s and the five’s.

I wonder why these fifth graders are still being quizzed on the multiplication tables. Are these just quick exercises to practice math facts? Is it an assessment to see which students haven’t learned them yet? If so, why would they test the entire class if only two or three students were lagging in this area?

We are located in an affluent NYC suburb where public school spending per pupil is about $19,000. If our students aren’t fluent in their math facts by fifth grade, we’re not getting our money’s worth. However, at least our students probably possess “deep conceptual understanding” and can apply lots of “higher order thinking skills”.

I really don’t know what to think. However, I have given up on believing class time is being used efficiently to teach the most important fundamental academic skills.

Wednesday, November 7, 2007

The Discover article on video games is the first popular journalism article I've seen that talks about the SEEKING emotion system in the brain, so-named by Jaak Panksepp, a neuroscientist in my pantheon of life-altering researcher-writers:

The genesis of this reaction may lie in the neurotransmitter dopamine. A number of studies have revealed that game playing triggers dopamine release in the brain, a finding that makes sense, given the instrumental role that dopamine plays in how the brain handles both reward and exploration. Jaak Panksepp, a neuroscientist collaborating with the Falk Center for Molecular Therapeutics at Northwestern University, calls the dopamine system the brain’s “seeking” circuitry, which propels us to explore new avenues for reward in our environment. The game world is teeming with objects that deliver clearly articulated rewards: more life, access to new levels, new equipment, new spells. Most of the crucial work in game interface design revolves around keeping players notified of potential rewards available to them and how much those rewards are needed.

If you create a system in which rewards are both clearly defined and achieved by exploring an environment, you’ll find human brains drawn to those systems, even if they’re made up of virtual characters and simulated sidewalks. It’s likely those Tactical Ops players in an fMRI machine were able to tolerate the physical discomfort of the machine because the game environment so powerfully stimulated the brain’s dopamine system.

Of course, dopamine is also involved in the addictiveness of drugs. “The thing to remember about dopamine is that it’s not at all the same thing as pleasure,” says Gregory Berns, a neuroscientist at Emory University School of Medicine in Atlanta, who looks at dopamine in a cultural context in his book, Satisfaction. “Dopamine is not the reward; it’s what lets you go out and explore in the first place. Without dopamine, you wouldn’t be able to learn properly.”

The SEEKING emotion is the biggie, as far as I can tell. It's one of the four core, hard-wired emotion systems in the brain. All mammals have it (I assume all living creatures must have it, but I don't know), and it drives most of the behaviors we engage in to stay alive, well, and interested in the goings-on about us.

My biggest surprise, when I first read Panksepp's chapter on SEEKING, is that curiosity isn't an intellectual property, as I'd always thought.

Curiosity is an emotion, one of the core emotions. Curiosity is SEEKING.

For years people thought the SEEKING system was the brain's "pleasure center." That's what I was taught. Psych courses used to regale undergraduates with tales of rats with electrodes implanted in their pleasure centers who would just keep pressing the lever to turn the current on until they died of starvation.

In October 2006 the Federation of American Scientists (FAS) endorsed video games as a potential means for teaching “higher-order thinking skills, such as strategic thinking, interpretive analysis, problem solving, plan formulation and execution, and adaptation to rapid change.”

The State Dept of Ed website has draft curriculum standards posted. If you are a Conn parent or educator, you might want to take a look at what they are doing. I haven't looked through these things carefully, but I want to get the links up here. The letter accompanying the draft standards invites feedback. I don't see why only educators should have fun with this, so please do take a look. The standards will be in draft form until December 2007.

The biggest change to the standards is the inclusion of "grade level expectations." These are fairly specific and are a big improvement over the old standards. For example, in 2nd grade, students should be able to order simple fractions, tell time to the 1/2 hour, and know the calendar months in order.

The standards are clear. They may not be very high, but they are at least clear.

But there are still too many standards. The mile wide inch deep criticism is even more apparent when you look at each of the tasks to be mastered along the way. Still too much pattern recognition, probability, and graphing in the earliest grades and not enough emphasis on automaticity with basic math facts and fluency with fractions, decimals, and percents in later elementary grades. It's there, but there's no focus and no sense of what is most critical. Because of the sheer number of standards and expectations, how is a teacher or school to wade through them all? If they give equal emphasis to everything, they will not master anything.

So a mixed bag, but a step in the right direction. If you have the time to look at these things, you might consider downloading the feedback form and e-mailing it in to the State Dept of Ed.

While bad teaching was incidental to the traditional method in earlier days, it has now become an inherent part of how much math is taught today. The NSF-sponsored texts with their emphasis on multiple algorithms, open-ended questions, top-down discovery and spiral learning force teachers to omit explicit instruction, although more experienced and knowledgable teachers may supplement (or supplant) such texts.

curriculum casualties

It is interesting therefore to learn that direct instruction and mastery learning are recommended methods of teaching for students with learning disabilities. (Rosenberg, et al., 2008) It is also interesting to note that over the past two decades, the number of students with learning disabilities has increased. In 2006, approximately 2.6 million students were identified with learning disabilities, more than three times as many as were identified in 1976-1977. Although one reason for this growth might be better means of diagnoses of specific disorders, there has still been growth. Between 1990 and 2004, 650,000 additional students were identified with learning disabilities, representing a 31% increase at a time when the overall student population grew by only 15%. (U.S. Department of Education, 2006).

I'm not sure how this relates to the increase in classified kids, but I suspect the causal relationship, assuming there is one, runs heavily in the direction of school failure causing diagnosis, as opposed to improved diagnosis causing drastically higher levels of SPED identification.

Also, I've been writing about psychiatric issues, including ADHD, which is often associated with LD, for many years now. I don't have the sense that there was at any point a sudden, enormous upswing in the ability to diagnose previously undiagnosed kids -- something that did take place with high-functioning autistic kids, I might add. One can find references to hyper kids going back at least to the 19th century; the "clinical" profile has been pretty familiar for a very long time.

The ADHD diagnosis did undergo one revolution thanks to John Ratey and Ned Hallowell, which was the recognition that ADHD afflicted adults as well as children. This recognition, along with Jimmy's diagnosis of autism, led John and me to write Shadow Syndromes.

I don't know the history of research on and diagnosis of dyslexia well. I do have the sense that there has been an enormous upswing in identification of dyslexia.

But that's the point.

ADHD, which we know can be associated with learning problems, has been recognized since at least the last century, and I don't believe we saw a sudden improvement in the ability to identify ADHD in elementary school kids in the past couple of decades.

In sharp contrast, it appears that we have seen a sudden and enormous upswing in the ability to identify "specific learning disabilities" such as dyslexia.

I believe Reid Lyon is right. We are looking at large numbers of children who are best considered "curriculum casualties." But the source of their problems has been misdiagnosed.

Instead of making the connection between bad teaching and bad learning, these children's failures to learn have been medicalized and handed off to special ed.

the question

Rosenberg et. al, also note that up to 50% of students with learning disabilities have been shown to overcome their learning difficulties when given high-quality instruction. Is the shift toward inquiry-based teaching resulting in more students being identified with learning disabilities? Are these students who in earlier days would have swum with the rest of the pack?

Brownell, spoken well of by NCTM and various luminaries in today's reform movement, was the key reformer of the early twentieth century and promoted what he called meaningful learning; i.e., teaching mathematics as a process, rather than a series of end products of isolated facts and procedures to be committed to memory.If this sounds like what the reformers are talking about today, it is because the complaints levied against how mathematics is taught, like the complaints about education in general through the years, have been perennial.What is often not mentioned when these complaints are "replayed" is that there have also been perennial solutions and some of these solutions have actually been effective.

Brownell led the charge against the isolated, rote-memory type of math teaching that came about in large part through the books and efforts of E. L. Thorndike, another figure of education at that time.The reformers listed above, including Brownell, all wrote math texts that were in use from the 30's through the 60's.The later books were written by Brownell (with Guy T. Buswell and Irene Sauble) starting in the mid-50's in a series called "Arithmetic We Need".I'm familiar with this series because they were the books I used when I was in school.I have copies of these and other books in use by all the authors.All the books give explanations of what is going on with specific mathematical procedures, and topics were presented in a logical sequence that allowed building upon previously learned and mastered material.But what is particularly interesting are the explanations in the teacher's manuals and prefaces to these books:

From "Making Sure of Arithmetic" (Grade 6):"Each new process is explained in the simplest terms, utilizing every graphic aid possible.From the beginning, meaning and relationship are emphasized.As a result the pupil gains not only skill but skill with understanding." (Morton, et. al., 1946)

From "The New Curriculum Arithmetics" (Grade 7) "A program of mixed and cumulative practice exercises insures mastery and retention of the processes and topics studied." (Brueckner, et al, 1941)

From "Growth in Arithmetic" (Grade 3):A comparison chart in the teacher's edition showing the difference between the older (Thorndike-derived) textbooks and this one: "Older: Taught as facts, skills, and habits of procedure; Newer: Taught to emphasize meanings, principles, and relationships. Facts and skills developed after understanding." (Clark, et al, 1952)

From "Teaching Arithmetic We Need" (Grade 5) "Each book in this series is built upon a conception of arithmetic that involves two aims, the social aim and the mathematical aim.Adherence to the latter aim requires that children see sense in what they learn."(Brownell, et. al.

[snip]

I would therefore add to the list of possible factors influencing the upward trends in achievement scores from the 40's through the mid-60's the textbooks in use, and the implementation of the theories behind them.This is not to say that the traditional math of such time was perfect.If I had to compare the "Arithmetic We Need" texts that I used with Saxon Math, or the math program used in Singapore, I would say the latter two are superior with much more challenging word problems.I can say, however, that the essentials of math were covered well, which would include place value, why a particular algorithm worked, thorough application of fractions and multiplication and division of fractions (similar to Singapore's approach) and application of procedures to solving word problems.Here are two problems from the sixth grade book of "Arithmetic We Need":

"How many glass containers holding 3/16 quarts can be filled with water from a quart bottle which is ¾ full?"

"If it takes 1and½hours to drive to the city,what part of the distance will Bill and his father drive in ¾ hour?"

Action research is not what usually comes to mind when we hear the word “research.” Action research is not a library project where we learn more about a topic that interests us. It is not problem-solving in the sense of trying to find out what is wrong, but rather a quest for knowledge about how to improve. Action research is not about doing research on or about people, or finding all available information on a topic looking for the correct answers. It involves people working to improve their skills, techniques, and strategies. Action research is not about learning why we do certain things, but rather how we can do things better. It is about how we can change our instruction to impact students.

The school board attorney who informally advises me has said that school culture is decidedly thin-skinned. I'd say this is a pretty good example of what "research" becomes when you want to look into things but it's illegal to find anything bad.

Speak no evil.

Love the idea that you would conduct no background research on purpose.

"Do ed schools give good training, at all, in how to do action research??"

This probably depends on the ed school, but in my experience, the training on action research was abundant -- ridiculously abundant. Here's a good pdf that explains action research:

This paper explains the birth of action research back in the '70s:

"Education practitioners questioned the applicability of scientific research designs and methodologies as a means to solve education issues. The results of many of these federally funded projects were seen as theoretical, not grounded in practice" (page 14).

To me, this is the red flag... Examining your own practice in a thoughtful, meaningful way is great -- and hopefully all teachers conduct this reflective research as a matter of course.

But educators shouldn't simultaneously dismiss the (admittedly scarce) solid quantitative research out there because it's "too theoretical." In my view, that's educational malpractice...and sadly very common in ed school.

Generally speaking, I'm not inclined to spend a lot of time bashing the 1970s just because....because I'm not. No particular reason.

But there's no question the decade produced a number of very bad ideas, Exhibit A being constructivism. It wasn't until recently that I understood what constructivism is in the broad sense of the term. Constructivism is what progressive education became after it encountered postructuralism.

Traditional progressive ed (now there's a neologism for you!) probably wouldn't have been to my taste, but I would take it any day over constructivism.

I received my BS Ed in May 2006, as a second career. I was not the oldest in my cohort, but the great majority were in their 20's. The school program was quite strong, although the advanced math education class was a sad example of what is happening in elementary education.

I was in a cohort of 15 or so students, and I was the only one who could actually do the math that the prof was showing us the ed. strategies for. She was a nationally certified curriculum adviser with a PhD. and kept telling the class: "You need to know how to do this math, I'm not here to teach you math." "You need to get some more math education before you step into a classroom."

She was amazed at how poor the student's skills were, although it was her first University level class. I wonder if her expectations have since declined.

Tuesday, November 6, 2007

A LOTTERY scratchcard has been withdrawn from sale by Camelot - because players couldn't understand it.

[snip]

To qualify for a prize, users had to scratch away a window to reveal a temperature lower than the figure displayed on each card. As the game had a winter theme, the temperature was usually below freezing.

But the concept of comparing negative numbers proved too difficult for some Camelot received dozens of complaints on the first day from players who could not understand how, for example, -5 is higher than -6.

Tina Farrell, from Levenshulme, called Camelot after failing to win with several cards.

The 23-year-old, who said she had left school without a maths GCSE, said: "On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card the machine said I hadn't.

"I phoned Camelot and they fobbed me off with some story that -6 is higher - not lower - than -8 but I'm not having it.

"I think Camelot are giving people the wrong impression - the card doesn't say to look for a colder or warmer temperature, it says to look for a higher or lower number. Six is a lower number than 8. Imagine how many people have been misled."

Well, I'm not laughing.

I can't figure out how to do the absolute value inequality word problem on C's homework tonight. Also, I can't figure out why it should be an absolute value problem in the first place.

In the TIMES today, NYC schools get their first value-added report cards:

The grades released yesterday contained many surprises, with some schools with top-notch reputations receiving B’s, C’s, D’s — and even F’s, to the astonishment of some parents.

That is because unlike traditional methods of judging schools, this one involves a complex calculation that assigns the most weight to how individual students improve in a year’s time on standardized state tests. It also compares schools with similar populations, as judged by demographics and incoming students’ test scores, and assigns final grades based on a curve. More than 60 percent of the schools earned A’s or B’s.

[snip]

Mr. Bloomberg said that the reports were devised to give parents crucial insight into their schools, and that if the grades upended longstanding school reputations, well, that was precisely the point. “We should be asking ourselves why some of the schools we thought were doing well aren’t serving students as effectively as other similar schools,” he said. Still, some parents lashed out at the enterprise, saying it overemphasized standardized tests.

“The way you treat our educators is part and parcel of the way you treat our students — constantly barraging them with narrow, deadening tests and demoralizing them with meaningless scores,” Jan Carr, whose son attends the Salk School of Science, a coveted Manhattan middle school that received a C, wrote in a letter to the chancellor.

[snip]

Several esteemed elementary schools that middle-class parents often factor in to their real estate decisions — including Public School 6 on the Upper East Side, P.S. 87 on the Upper West Side, P.S. 234 in TriBeCa and P.S. 321 in Park Slope, Brooklyn, — received B’s. Other popular schools fared worse. P.S. 154 in Windsor Terrace, Brooklyn, received a D, as did Central Park East I in Harlem.

A whole lotta tutors there at P.S. 234, and they still swing only a B.

The fact is in District 2 our kids are learning math like champs. Our scores are extraordinary,” said Daria Rigny, District 2 superintendent.

But the whispers in the schoolyards are that the high scores owe much to the widespread use of tutors.

“If you just studied TERC and took the test for Stuyvesant you wouldn’t be prepared. The only way is to be tutored,” said Jonathan Levine, the father of one current and two former P.S. 234 students. He says this makes two tracks, those who tutor and those who don’t.

One math tutor who works with many Downtown kids said most of her students are 4th and 5th graders whose parents worry that they will be unprepared for state tests and middle school. “They don’t even tell me what it is they want them to learn. They just say ‘could you teach them the math that I learned?”’ The tutor, who did not want to be identified, said some kids do struggle with TERC. “They try to show me how they solve problems in their classes and half the time they don’t understand it.”

I still don't see how value-added assessment adequately controls for tutors.

Monday, November 5, 2007

The nation’s 1,206 schools, colleges and departments of education constitute a sprawling enterprise, located at 78 percent of all four-year colleges and universities. They award one out of every 12 bachelor’s diplomas; a quarter of all master’s degrees; and 15 percent of all doctorates, more than any other branch of the academy.

The rationale offered by [NCLB] authors: After almost 20 years of educational reform, the country needed to know which of the myriad policies and practices that had been tried actually worked. This required rigorous, scientifically based research relying principally on random controlled trials, the gold standard for research studies. The authors of NCLB believed there was a paucity of such research in education at the time the bill became law.

The federal research prescription brought a loud and impassioned response from the education community. Since the passage of NCLB, we have heard critics reject the prescribed methodology of “scientifically based research” and the accompanying assessment of the condition of education research. The new research requirements are characterized as representing ideological censorship and opposition to the liberality of education schools. What No Child Left Behind termed “scientifically based research” was the most expensive form of research, which few education schools could afford. Qualitative research, the most common methodology in education and one rejected as not scientifically based, was said to be a more appropriate way to answer some research questions.

There also have been conspiracy theories: The Republican White House and Congress created the new requirements to shift research funding from education schools to conservative think tanks.

etc.

Interestingly, the report says that there are more good programs teaching education research than there are good teacher education program.

Nobody working in the public schools is reading these journals anyway, which may be just as well:

Education research is likewise connected only weakly with practice. School administrators interviewed in the course of this study were regularly asked which education publications they read. The most common answers were Education Week, the trade paper, and publications from their own professional associations, such as unions and principals’ organizations. Almost never did they say they read scholarly journals; and when they did, the person being interviewed was invariably enrolled in a graduate program.

I suppose the fact that school administrators apparently do not know the difference between a trade paper and a refereed journal may explain the enthusiasm for Google as a curriculum.

threat level rising to red

The current issue of the Journal of Learning Sciences has an article on math ed:

College administrators grumble about the rise of "helicopter parents," moms and dads who keep hovering over the lives of their children even after they leave for college.

But helicopter parents aren't just hovering. They're swooping down in attack mode.

Having established the rising horror of helicopter parents (when I wrote for New Woman I always had to say that whatever I was writing about was "skyrocketing"), the article goes on to report survey data that directly contradicts the lead (I never did that, of course):

There's an upside to intervening parents. Their children are more engaged in college life, happier and reporting getting more from the experience.

"We speculate maybe these students are persisting and taking advantage of a lot of opportunities in college, when they might not have done that if their parents weren't prodding," Kuh said.

It sounds as if "helicopter parenting" in college happens for the same reason it does in K-12, which is students not doing well:

"We speculate maybe these students are persisting and taking advantage of a lot of opportunities in college, when they might not have done that if their parents weren't prodding," Kuh said. However, those students do get lower grades.

Barbara Hofer, a psychologist at Middlebury College in Vermont, said the results are similar to data she has gathered but not yet published on students at Middlebury and the University of Michigan.

[snip]

Like the NSSE survey, Hofer has also discovered communication stays constant through college (about 13 times per week, by phone and electronically, for both freshmen and seniors), and that students who are more independent about academics had higher GPAs. However, it's unclear whether that's cause or effect: Does laissez-faire parenting produce smarter students, or do students who struggle academically draw in their parents for help?

Interestingly, while I've read Steinberg's book, I hadn't remembered that parental involvement in the schools works only for "authoritative" parents, not permissive parents.

Abstract

This article examines the impact of authoritative parenting, parental involvement in schooling, and parental encouragement to succeed on adolescent school achievement in an ethnically and socio-economically heterogeneous sample of approximately 6,400 American 14-18-year-olds.

[snip]

Authoritative parenting (high acceptance, supervision, and psychological autonomy granting) leads to better adolescent school performance and stronger school engagement. The positive impact of authoritative parenting on adolescent achievement, however, is mediated by the positive effect of authoritativeness on parental involvement in schooling. In addition, nonauthoritativeness attenuates the beneficial impact of parental involvement in schooling on adolescent achievement. Parental involvement is much more likely to promote adolescent school success when it occurs in the context of an authoritative home environment.

This makes me chuckle.

All along I've had the sense that hammering your school doesn't do any good if you aren't also hammering your kid -- and research proves it!

The first installment argues that school performance increased steadily from roughly 1940 to 1965, then declined "dramatically."

This coincides with first-person accounts I've heard or read. I remember once reading Milton Friedman saying he'd had a good education in public schools; Alan Greenspan says the same.

At the dentist awhile back, I talked to a man in his 70s who had attended NYC public schools. He said they were great, and gave me the list of subjects they studied. The h.s. math courses were obviously advanced.

Same thing for the decline that began in the 60s.

Ed's high school was terrific; the same high school had declined significantly by the time his youngest brother enrolled. And my grandmother, who returned to teaching sometime in the 1960s, told my mom that there had been a complete change in the kind of person who became a teacher, and not for the better.

Still, I'd never heard that schools improved for 15 years running -- or that that improvement immediately preceded a sharp decline.

Seems terrifically useful, probably the single most useful book I have on Singapore Math apart from the textbooks and assessment books (that's workbooks in Singaporean* according to lrg) themselves. Only 150 pages in all, and many of those pages are simply practice problems. On the other hand, I'm not sure this book has problems at the "Challenging" level contained in the Challenging Word Problems books.

This is the second book I've seen that teaches U.S. teachers the bar model method, Sybilla Beckmann's college textbook being the first. I'm thinking we may begin to see bar models incorporated into U.S. texts and classrooms.

Dan Greene of Downtown College Prep is teaching them to his "numeracy" students.